Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B

Percentage Accurate: 85.2% → 98.1%

Time: 13.4s

Alternatives: 14

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(z - t\right)}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (a - t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / (a - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (a - t));
}

Python

def code(x, y, z, t, a):
	return x + ((y * (z - t)) / (a - t))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y * (z - t)) / (a - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 85.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y \cdot \left(z - t\right)}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ (* y (- z t)) (- a t))))

C

double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (a - t));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + ((y * (z - t)) / (a - t))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + ((y * (z - t)) / (a - t));
}

Python

def code(x, y, z, t, a):
	return x + ((y * (z - t)) / (a - t))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t)))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + ((y * (z - t)) / (a - t));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 98.1% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= (+ x (/ (* y (- z t)) (- a t))) -1e-8)
   (fma (/ y (- a t)) (- z t) x)
   (+ x (* y (/ (- z t) (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((x + ((y * (z - t)) / (a - t))) <= -1e-8) {
		tmp = fma((y / (a - t)), (z - t), x);
	} else {
		tmp = x + (y * ((z - t) / (a - t)));
	}
	return tmp;
}

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (Float64(x + Float64(Float64(y * Float64(z - t)) / Float64(a - t))) <= -1e-8)
		tmp = fma(Float64(y / Float64(a - t)), Float64(z - t), x);
	else
		tmp = Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))));
	end
	return tmp
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[N[(x + N[(N[(y * N[(z - t), $MachinePrecision]), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1e-8], N[(N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision] * N[(z - t), $MachinePrecision] + x), $MachinePrecision], N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))) < -1e-8

   1. Initial program 80.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 80.3%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 100.0%

         \[\leadsto \color{blue}{\frac{y}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 100.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing

   if -1e-8 < (+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))

   1. Initial program 87.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 99.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y}}} \]

      2. associate-/r/ 99.8%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{z - t}} \cdot y} \]

      3. clear-num 99.9%

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t}} \cdot y \]

   6. Applied egg-rr 99.9%

      \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - t\right)}{a - t} \leq -1 \cdot 10^{-8}:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z - t}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 76.0% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ t_2 := x - \frac{y}{\frac{t}{z}}\\ \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+42}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-15}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-68}:\\ \;\;\;\;t\_2\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83} \lor \neg \left(t \leq 1360\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))) (t_2 (- x (/ y (/ t z)))))
   (if (<= t -6.5e+186)
     (+ x y)
     (if (<= t -2e+42)
       t_2
       (if (<= t -9.6e-15)
         t_1
         (if (<= t -4.8e-68)
           t_2
           (if (or (<= t -7.5e-83) (not (<= t 1360.0))) (+ x y) t_1)))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = x - (y / (t / z));
	double tmp;
	if (t <= -6.5e+186) {
		tmp = x + y;
	} else if (t <= -2e+42) {
		tmp = t_2;
	} else if (t <= -9.6e-15) {
		tmp = t_1;
	} else if (t <= -4.8e-68) {
		tmp = t_2;
	} else if ((t <= -7.5e-83) || !(t <= 1360.0)) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    t_2 = x - (y / (t / z))
    if (t <= (-6.5d+186)) then
        tmp = x + y
    else if (t <= (-2d+42)) then
        tmp = t_2
    else if (t <= (-9.6d-15)) then
        tmp = t_1
    else if (t <= (-4.8d-68)) then
        tmp = t_2
    else if ((t <= (-7.5d-83)) .or. (.not. (t <= 1360.0d0))) then
        tmp = x + y
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double t_2 = x - (y / (t / z));
	double tmp;
	if (t <= -6.5e+186) {
		tmp = x + y;
	} else if (t <= -2e+42) {
		tmp = t_2;
	} else if (t <= -9.6e-15) {
		tmp = t_1;
	} else if (t <= -4.8e-68) {
		tmp = t_2;
	} else if ((t <= -7.5e-83) || !(t <= 1360.0)) {
		tmp = x + y;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	t_2 = x - (y / (t / z))
	tmp = 0
	if t <= -6.5e+186:
		tmp = x + y
	elif t <= -2e+42:
		tmp = t_2
	elif t <= -9.6e-15:
		tmp = t_1
	elif t <= -4.8e-68:
		tmp = t_2
	elif (t <= -7.5e-83) or not (t <= 1360.0):
		tmp = x + y
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	t_2 = Float64(x - Float64(y / Float64(t / z)))
	tmp = 0.0
	if (t <= -6.5e+186)
		tmp = Float64(x + y);
	elseif (t <= -2e+42)
		tmp = t_2;
	elseif (t <= -9.6e-15)
		tmp = t_1;
	elseif (t <= -4.8e-68)
		tmp = t_2;
	elseif ((t <= -7.5e-83) || !(t <= 1360.0))
		tmp = Float64(x + y);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	t_2 = x - (y / (t / z));
	tmp = 0.0;
	if (t <= -6.5e+186)
		tmp = x + y;
	elseif (t <= -2e+42)
		tmp = t_2;
	elseif (t <= -9.6e-15)
		tmp = t_1;
	elseif (t <= -4.8e-68)
		tmp = t_2;
	elseif ((t <= -7.5e-83) || ~((t <= 1360.0)))
		tmp = x + y;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t, -6.5e+186], N[(x + y), $MachinePrecision], If[LessEqual[t, -2e+42], t$95$2, If[LessEqual[t, -9.6e-15], t$95$1, If[LessEqual[t, -4.8e-68], t$95$2, If[Or[LessEqual[t, -7.5e-83], N[Not[LessEqual[t, 1360.0]], $MachinePrecision]], N[(x + y), $MachinePrecision], t$95$1]]]]]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999997e186 or -4.79999999999999982e-68 < t < -7.4999999999999997e-83 or 1360 < t

   1. Initial program 66.1%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 79.4%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 79.4%

         \[\leadsto \color{blue}{y + x} \]

   7. Simplified 79.4%

      \[\leadsto \color{blue}{y + x} \]

   if -6.4999999999999997e186 < t < -2.00000000000000009e42 or -9.5999999999999998e-15 < t < -4.79999999999999982e-68

   1. Initial program 91.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 81.0%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a - t}} \]

   6. Taylor expanded in a around 0 76.9%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{y \cdot z}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 76.9%

         \[\leadsto x + \color{blue}{\left(-\frac{y \cdot z}{t}\right)} \]

      2. unsub-neg 76.9%

         \[\leadsto \color{blue}{x - \frac{y \cdot z}{t}} \]

      3. associate-/l* 79.8%

         \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{z}}} \]

   8. Simplified 79.8%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{t}{z}}} \]

   if -2.00000000000000009e42 < t < -9.5999999999999998e-15 or -7.4999999999999997e-83 < t < 1360

   1. Initial program 94.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 95.6%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 79.4%

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{a}} \]
   6. Step-by-step derivation

      1. +-commutative 79.4%

         \[\leadsto \color{blue}{\frac{y \cdot z}{a} + x} \]

      2. associate-/l* 80.7%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} + x \]

   7. Simplified 80.7%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}} + x} \]
   8. Step-by-step derivation

      1. associate-/r/ 83.5%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} + x \]

   9. Applied egg-rr 83.5%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot z} + x \]
3. Recombined 3 regimes into one program.

4. Final simplification 81.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq -2 \cdot 10^{+42}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -9.6 \cdot 10^{-15}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;t \leq -4.8 \cdot 10^{-68}:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;t \leq -7.5 \cdot 10^{-83} \lor \neg \left(t \leq 1360\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 69.2% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := x + z \cdot \frac{y}{a}\\ \mathbf{if}\;x \leq -7.6 \cdot 10^{+236}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq -88:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-156}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (+ x (* z (/ y a)))))
   (if (<= x -7.6e+236)
     t_1
     (if (<= x -88.0)
       (- x (/ y (/ t z)))
       (if (<= x -2.9e-49)
         (+ x y)
         (if (<= x 1.85e-156) (* (- z t) (/ y (- a t))) t_1))))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (x <= -7.6e+236) {
		tmp = t_1;
	} else if (x <= -88.0) {
		tmp = x - (y / (t / z));
	} else if (x <= -2.9e-49) {
		tmp = x + y;
	} else if (x <= 1.85e-156) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = x + (z * (y / a))
    if (x <= (-7.6d+236)) then
        tmp = t_1
    else if (x <= (-88.0d0)) then
        tmp = x - (y / (t / z))
    else if (x <= (-2.9d-49)) then
        tmp = x + y
    else if (x <= 1.85d-156) then
        tmp = (z - t) * (y / (a - t))
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = x + (z * (y / a));
	double tmp;
	if (x <= -7.6e+236) {
		tmp = t_1;
	} else if (x <= -88.0) {
		tmp = x - (y / (t / z));
	} else if (x <= -2.9e-49) {
		tmp = x + y;
	} else if (x <= 1.85e-156) {
		tmp = (z - t) * (y / (a - t));
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = x + (z * (y / a))
	tmp = 0
	if x <= -7.6e+236:
		tmp = t_1
	elif x <= -88.0:
		tmp = x - (y / (t / z))
	elif x <= -2.9e-49:
		tmp = x + y
	elif x <= 1.85e-156:
		tmp = (z - t) * (y / (a - t))
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(x + Float64(z * Float64(y / a)))
	tmp = 0.0
	if (x <= -7.6e+236)
		tmp = t_1;
	elseif (x <= -88.0)
		tmp = Float64(x - Float64(y / Float64(t / z)));
	elseif (x <= -2.9e-49)
		tmp = Float64(x + y);
	elseif (x <= 1.85e-156)
		tmp = Float64(Float64(z - t) * Float64(y / Float64(a - t)));
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = x + (z * (y / a));
	tmp = 0.0;
	if (x <= -7.6e+236)
		tmp = t_1;
	elseif (x <= -88.0)
		tmp = x - (y / (t / z));
	elseif (x <= -2.9e-49)
		tmp = x + y;
	elseif (x <= 1.85e-156)
		tmp = (z - t) * (y / (a - t));
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -7.6e+236], t$95$1, If[LessEqual[x, -88.0], N[(x - N[(y / N[(t / z), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, -2.9e-49], N[(x + y), $MachinePrecision], If[LessEqual[x, 1.85e-156], N[(N[(z - t), $MachinePrecision] * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$1]]]]]

Derivation

1. Split input into 4 regimes

2. if x < -7.59999999999999973e236 or 1.85e-156 < x

   1. Initial program 87.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 95.4%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 95.4%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 74.8%

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{a}} \]
   6. Step-by-step derivation

      1. +-commutative 74.8%

         \[\leadsto \color{blue}{\frac{y \cdot z}{a} + x} \]

      2. associate-/l* 73.2%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} + x \]

   7. Simplified 73.2%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}} + x} \]
   8. Step-by-step derivation

      1. associate-/r/ 78.4%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} + x \]

   9. Applied egg-rr 78.4%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot z} + x \]

   if -7.59999999999999973e236 < x < -88

   1. Initial program 89.5%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 97.8%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 97.8%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 93.7%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a - t}} \]

   6. Taylor expanded in a around 0 74.7%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{y \cdot z}{t}} \]
   7. Step-by-step derivation

      1. mul-1-neg 74.7%

         \[\leadsto x + \color{blue}{\left(-\frac{y \cdot z}{t}\right)} \]

      2. unsub-neg 74.7%

         \[\leadsto \color{blue}{x - \frac{y \cdot z}{t}} \]

      3. associate-/l* 74.7%

         \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{z}}} \]

   8. Simplified 74.7%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{t}{z}}} \]

   if -88 < x < -2.9e-49

   1. Initial program 79.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 100.0%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 79.7%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 79.7%

         \[\leadsto \color{blue}{y + x} \]

   7. Simplified 79.7%

      \[\leadsto \color{blue}{y + x} \]

   if -2.9e-49 < x < 1.85e-156

   1. Initial program 78.6%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 78.6%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 95.1%

         \[\leadsto \color{blue}{\frac{y}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 95.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)} \]

   3. Simplified 95.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 93.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right) \]

      2. inv-pow 93.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\frac{a - t}{y}\right)}^{-1}}, z - t, x\right) \]

   6. Applied egg-rr 93.2%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\frac{a - t}{y}\right)}^{-1}}, z - t, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 93.2%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right) \]

   8. Simplified 93.2%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right) \]

   9. Taylor expanded in y around -inf 64.2%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   10. Step-by-step derivation

       1. associate-*l/ 80.7%

          \[\leadsto \color{blue}{\frac{y}{a - t} \cdot \left(z - t\right)} \]

       2. *-commutative 80.7%

          \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   11. Simplified 80.7%

       \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 78.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.6 \cdot 10^{+236}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \mathbf{elif}\;x \leq -88:\\ \;\;\;\;x - \frac{y}{\frac{t}{z}}\\ \mathbf{elif}\;x \leq -2.9 \cdot 10^{-49}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-156}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 63.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+212} \lor \neg \left(z \leq 5.2 \cdot 10^{+42}\right) \land \left(z \leq 9.5 \cdot 10^{+144} \lor \neg \left(z \leq 6 \cdot 10^{+182}\right)\right):\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= z -5.2e+212)
         (and (not (<= z 5.2e+42)) (or (<= z 9.5e+144) (not (<= z 6e+182)))))
   (* z (/ y (- a t)))
   (+ x y)))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+212) || (!(z <= 5.2e+42) && ((z <= 9.5e+144) || !(z <= 6e+182)))) {
		tmp = z * (y / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((z <= (-5.2d+212)) .or. (.not. (z <= 5.2d+42)) .and. (z <= 9.5d+144) .or. (.not. (z <= 6d+182))) then
        tmp = z * (y / (a - t))
    else
        tmp = x + y
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((z <= -5.2e+212) || (!(z <= 5.2e+42) && ((z <= 9.5e+144) || !(z <= 6e+182)))) {
		tmp = z * (y / (a - t));
	} else {
		tmp = x + y;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (z <= -5.2e+212) or (not (z <= 5.2e+42) and ((z <= 9.5e+144) or not (z <= 6e+182))):
		tmp = z * (y / (a - t))
	else:
		tmp = x + y
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((z <= -5.2e+212) || (!(z <= 5.2e+42) && ((z <= 9.5e+144) || !(z <= 6e+182))))
		tmp = Float64(z * Float64(y / Float64(a - t)));
	else
		tmp = Float64(x + y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((z <= -5.2e+212) || (~((z <= 5.2e+42)) && ((z <= 9.5e+144) || ~((z <= 6e+182)))))
		tmp = z * (y / (a - t));
	else
		tmp = x + y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[z, -5.2e+212], And[N[Not[LessEqual[z, 5.2e+42]], $MachinePrecision], Or[LessEqual[z, 9.5e+144], N[Not[LessEqual[z, 6e+182]], $MachinePrecision]]]], N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if z < -5.1999999999999997e212 or 5.1999999999999998e42 < z < 9.50000000000000031e144 or 6.0000000000000004e182 < z

   1. Initial program 80.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 80.4%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 97.0%

         \[\leadsto \color{blue}{\frac{y}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 97.0%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)} \]

   3. Simplified 97.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 97.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right) \]

      2. inv-pow 97.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\frac{a - t}{y}\right)}^{-1}}, z - t, x\right) \]

   6. Applied egg-rr 97.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\frac{a - t}{y}\right)}^{-1}}, z - t, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 97.0%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right) \]

   8. Simplified 97.0%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right) \]

   9. Taylor expanded in z around inf 63.9%

      \[\leadsto \color{blue}{\frac{y \cdot z}{a - t}} \]
   10. Step-by-step derivation

       1. *-commutative 63.9%

          \[\leadsto \frac{\color{blue}{z \cdot y}}{a - t} \]

       2. associate-*r/ 73.4%

          \[\leadsto \color{blue}{z \cdot \frac{y}{a - t}} \]

   11. Simplified 73.4%

       \[\leadsto \color{blue}{z \cdot \frac{y}{a - t}} \]

   if -5.1999999999999997e212 < z < 5.1999999999999998e42 or 9.50000000000000031e144 < z < 6.0000000000000004e182

   1. Initial program 86.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 98.3%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 98.3%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 67.6%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 67.6%

         \[\leadsto \color{blue}{y + x} \]

   7. Simplified 67.6%

      \[\leadsto \color{blue}{y + x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 69.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;z \leq -5.2 \cdot 10^{+212} \lor \neg \left(z \leq 5.2 \cdot 10^{+42}\right) \land \left(z \leq 9.5 \cdot 10^{+144} \lor \neg \left(z \leq 6 \cdot 10^{+182}\right)\right):\\ \;\;\;\;z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + y\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 80.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a - t}\\ \mathbf{if}\;x \leq -9.2 \cdot 10^{-75} \lor \neg \left(x \leq 1.75 \cdot 10^{-170}\right):\\ \;\;\;\;x + z \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- a t))))
   (if (or (<= x -9.2e-75) (not (<= x 1.75e-170)))
     (+ x (* z t_1))
     (* (- z t) t_1))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - t);
	double tmp;
	if ((x <= -9.2e-75) || !(x <= 1.75e-170)) {
		tmp = x + (z * t_1);
	} else {
		tmp = (z - t) * t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (a - t)
    if ((x <= (-9.2d-75)) .or. (.not. (x <= 1.75d-170))) then
        tmp = x + (z * t_1)
    else
        tmp = (z - t) * t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - t);
	double tmp;
	if ((x <= -9.2e-75) || !(x <= 1.75e-170)) {
		tmp = x + (z * t_1);
	} else {
		tmp = (z - t) * t_1;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a - t)
	tmp = 0
	if (x <= -9.2e-75) or not (x <= 1.75e-170):
		tmp = x + (z * t_1)
	else:
		tmp = (z - t) * t_1
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a - t))
	tmp = 0.0
	if ((x <= -9.2e-75) || !(x <= 1.75e-170))
		tmp = Float64(x + Float64(z * t_1));
	else
		tmp = Float64(Float64(z - t) * t_1);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a - t);
	tmp = 0.0;
	if ((x <= -9.2e-75) || ~((x <= 1.75e-170)))
		tmp = x + (z * t_1);
	else
		tmp = (z - t) * t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[x, -9.2e-75], N[Not[LessEqual[x, 1.75e-170]], $MachinePrecision]], N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision], N[(N[(z - t), $MachinePrecision] * t$95$1), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if x < -9.2e-75 or 1.74999999999999992e-170 < x

   1. Initial program 87.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.6%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.6%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 85.6%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a - t}} \]
   6. Step-by-step derivation

      1. associate-*l/ 90.0%

         \[\leadsto x + \color{blue}{\frac{y}{a - t} \cdot z} \]

      2. *-commutative 90.0%

         \[\leadsto x + \color{blue}{z \cdot \frac{y}{a - t}} \]

   7. Simplified 90.0%

      \[\leadsto x + \color{blue}{z \cdot \frac{y}{a - t}} \]

   if -9.2e-75 < x < 1.74999999999999992e-170

   1. Initial program 77.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. +-commutative 77.7%

         \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t} + x} \]

      2. associate-*l/ 95.8%

         \[\leadsto \color{blue}{\frac{y}{a - t} \cdot \left(z - t\right)} + x \]

      3. fma-def 95.8%

         \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)} \]

   3. Simplified 95.8%

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{a - t}, z - t, x\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 93.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right) \]

      2. inv-pow 93.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\frac{a - t}{y}\right)}^{-1}}, z - t, x\right) \]

   6. Applied egg-rr 93.7%

      \[\leadsto \mathsf{fma}\left(\color{blue}{{\left(\frac{a - t}{y}\right)}^{-1}}, z - t, x\right) \]
   7. Step-by-step derivation

      1. unpow-1 93.7%

         \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right) \]

   8. Simplified 93.7%

      \[\leadsto \mathsf{fma}\left(\color{blue}{\frac{1}{\frac{a - t}{y}}}, z - t, x\right) \]

   9. Taylor expanded in y around -inf 64.1%

      \[\leadsto \color{blue}{\frac{y \cdot \left(z - t\right)}{a - t}} \]
   10. Step-by-step derivation

       1. associate-*l/ 82.2%

          \[\leadsto \color{blue}{\frac{y}{a - t} \cdot \left(z - t\right)} \]

       2. *-commutative 82.2%

          \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]

   11. Simplified 82.2%

       \[\leadsto \color{blue}{\left(z - t\right) \cdot \frac{y}{a - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 87.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -9.2 \cdot 10^{-75} \lor \neg \left(x \leq 1.75 \cdot 10^{-170}\right):\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;\left(z - t\right) \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.2% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_1 := \frac{y}{a - t}\\ \mathbf{if}\;t \leq -3.2 \cdot 10^{+109} \lor \neg \left(t \leq 3.1 \cdot 10^{+125}\right):\\ \;\;\;\;x - t \cdot t\_1\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (let* ((t_1 (/ y (- a t))))
   (if (or (<= t -3.2e+109) (not (<= t 3.1e+125)))
     (- x (* t t_1))
     (+ x (* z t_1)))))

C

double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - t);
	double tmp;
	if ((t <= -3.2e+109) || !(t <= 3.1e+125)) {
		tmp = x - (t * t_1);
	} else {
		tmp = x + (z * t_1);
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: t_1
    real(8) :: tmp
    t_1 = y / (a - t)
    if ((t <= (-3.2d+109)) .or. (.not. (t <= 3.1d+125))) then
        tmp = x - (t * t_1)
    else
        tmp = x + (z * t_1)
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double t_1 = y / (a - t);
	double tmp;
	if ((t <= -3.2e+109) || !(t <= 3.1e+125)) {
		tmp = x - (t * t_1);
	} else {
		tmp = x + (z * t_1);
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	t_1 = y / (a - t)
	tmp = 0
	if (t <= -3.2e+109) or not (t <= 3.1e+125):
		tmp = x - (t * t_1)
	else:
		tmp = x + (z * t_1)
	return tmp

Julia

function code(x, y, z, t, a)
	t_1 = Float64(y / Float64(a - t))
	tmp = 0.0
	if ((t <= -3.2e+109) || !(t <= 3.1e+125))
		tmp = Float64(x - Float64(t * t_1));
	else
		tmp = Float64(x + Float64(z * t_1));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	t_1 = y / (a - t);
	tmp = 0.0;
	if ((t <= -3.2e+109) || ~((t <= 3.1e+125)))
		tmp = x - (t * t_1);
	else
		tmp = x + (z * t_1);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := Block[{t$95$1 = N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t, -3.2e+109], N[Not[LessEqual[t, 3.1e+125]], $MachinePrecision]], N[(x - N[(t * t$95$1), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * t$95$1), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if t < -3.2000000000000001e109 or 3.1e125 < t

   1. Initial program 61.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 55.9%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{t \cdot y}{a - t}} \]
   6. Step-by-step derivation

      1. associate-*r/ 55.9%

         \[\leadsto x + \color{blue}{\frac{-1 \cdot \left(t \cdot y\right)}{a - t}} \]

      2. mul-1-neg 55.9%

         \[\leadsto x + \frac{\color{blue}{-t \cdot y}}{a - t} \]

      3. distribute-lft-neg-out 55.9%

         \[\leadsto x + \frac{\color{blue}{\left(-t\right) \cdot y}}{a - t} \]

      4. associate-*r/ 90.5%

         \[\leadsto x + \color{blue}{\left(-t\right) \cdot \frac{y}{a - t}} \]

      5. distribute-lft-neg-out 90.5%

         \[\leadsto x + \color{blue}{\left(-t \cdot \frac{y}{a - t}\right)} \]

      6. unsub-neg 90.5%

         \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   7. Simplified 90.5%

      \[\leadsto \color{blue}{x - t \cdot \frac{y}{a - t}} \]

   if -3.2000000000000001e109 < t < 3.1e125

   1. Initial program 95.2%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.5%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.5%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 86.9%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a - t}} \]
   6. Step-by-step derivation

      1. associate-*l/ 89.5%

         \[\leadsto x + \color{blue}{\frac{y}{a - t} \cdot z} \]

      2. *-commutative 89.5%

         \[\leadsto x + \color{blue}{z \cdot \frac{y}{a - t}} \]

   7. Simplified 89.5%

      \[\leadsto x + \color{blue}{z \cdot \frac{y}{a - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -3.2 \cdot 10^{+109} \lor \neg \left(t \leq 3.1 \cdot 10^{+125}\right):\\ \;\;\;\;x - t \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.0074 \lor \neg \left(t \leq 1.45 \cdot 10^{+76}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.0074) (not (<= t 1.45e+76)))
   (- x (/ y (/ t (- z t))))
   (+ x (* z (/ y (- a t))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.0074) || !(t <= 1.45e+76)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-0.0074d0)) .or. (.not. (t <= 1.45d+76))) then
        tmp = x - (y / (t / (z - t)))
    else
        tmp = x + (z * (y / (a - t)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.0074) || !(t <= 1.45e+76)) {
		tmp = x - (y / (t / (z - t)));
	} else {
		tmp = x + (z * (y / (a - t)));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.0074) or not (t <= 1.45e+76):
		tmp = x - (y / (t / (z - t)))
	else:
		tmp = x + (z * (y / (a - t)))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.0074) || !(t <= 1.45e+76))
		tmp = Float64(x - Float64(y / Float64(t / Float64(z - t))));
	else
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.0074) || ~((t <= 1.45e+76)))
		tmp = x - (y / (t / (z - t)));
	else
		tmp = x + (z * (y / (a - t)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.0074], N[Not[LessEqual[t, 1.45e+76]], $MachinePrecision]], N[(x - N[(y / N[(t / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0074000000000000003 or 1.4500000000000001e76 < t

   1. Initial program 70.4%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in a around 0 65.3%

      \[\leadsto \color{blue}{x + -1 \cdot \frac{y \cdot \left(z - t\right)}{t}} \]
   6. Step-by-step derivation

      1. mul-1-neg 65.3%

         \[\leadsto x + \color{blue}{\left(-\frac{y \cdot \left(z - t\right)}{t}\right)} \]

      2. unsub-neg 65.3%

         \[\leadsto \color{blue}{x - \frac{y \cdot \left(z - t\right)}{t}} \]

      3. associate-/l* 90.5%

         \[\leadsto x - \color{blue}{\frac{y}{\frac{t}{z - t}}} \]

   7. Simplified 90.5%

      \[\leadsto \color{blue}{x - \frac{y}{\frac{t}{z - t}}} \]

   if -0.0074000000000000003 < t < 1.4500000000000001e76

   1. Initial program 94.9%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 95.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 95.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 88.1%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a - t}} \]
   6. Step-by-step derivation

      1. associate-*l/ 92.5%

         \[\leadsto x + \color{blue}{\frac{y}{a - t} \cdot z} \]

      2. *-commutative 92.5%

         \[\leadsto x + \color{blue}{z \cdot \frac{y}{a - t}} \]

   7. Simplified 92.5%

      \[\leadsto x + \color{blue}{z \cdot \frac{y}{a - t}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 91.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.0074 \lor \neg \left(t \leq 1.45 \cdot 10^{+76}\right):\\ \;\;\;\;x - \frac{y}{\frac{t}{z - t}}\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 84.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+123}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t - a}{y}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (<= t -6.5e+186)
   (+ x y)
   (if (<= t 3.2e+123) (+ x (* z (/ y (- a t)))) (+ x (/ t (/ (- t a) y))))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+186) {
		tmp = x + y;
	} else if (t <= 3.2e+123) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (t / ((t - a) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (t <= (-6.5d+186)) then
        tmp = x + y
    else if (t <= 3.2d+123) then
        tmp = x + (z * (y / (a - t)))
    else
        tmp = x + (t / ((t - a) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (t <= -6.5e+186) {
		tmp = x + y;
	} else if (t <= 3.2e+123) {
		tmp = x + (z * (y / (a - t)));
	} else {
		tmp = x + (t / ((t - a) / y));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if t <= -6.5e+186:
		tmp = x + y
	elif t <= 3.2e+123:
		tmp = x + (z * (y / (a - t)))
	else:
		tmp = x + (t / ((t - a) / y))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (t <= -6.5e+186)
		tmp = Float64(x + y);
	elseif (t <= 3.2e+123)
		tmp = Float64(x + Float64(z * Float64(y / Float64(a - t))));
	else
		tmp = Float64(x + Float64(t / Float64(Float64(t - a) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (t <= -6.5e+186)
		tmp = x + y;
	elseif (t <= 3.2e+123)
		tmp = x + (z * (y / (a - t)));
	else
		tmp = x + (t / ((t - a) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[t, -6.5e+186], N[(x + y), $MachinePrecision], If[LessEqual[t, 3.2e+123], N[(x + N[(z * N[(y / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(t / N[(N[(t - a), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if t < -6.4999999999999997e186

   1. Initial program 51.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 92.3%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 92.3%

         \[\leadsto \color{blue}{y + x} \]

   7. Simplified 92.3%

      \[\leadsto \color{blue}{y + x} \]

   if -6.4999999999999997e186 < t < 3.20000000000000005e123

   1. Initial program 94.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 96.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 96.7%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around inf 86.2%

      \[\leadsto x + \color{blue}{\frac{y \cdot z}{a - t}} \]
   6. Step-by-step derivation

      1. associate-*l/ 88.7%

         \[\leadsto x + \color{blue}{\frac{y}{a - t} \cdot z} \]

      2. *-commutative 88.7%

         \[\leadsto x + \color{blue}{z \cdot \frac{y}{a - t}} \]

   7. Simplified 88.7%

      \[\leadsto x + \color{blue}{z \cdot \frac{y}{a - t}} \]

   if 3.20000000000000005e123 < t

   1. Initial program 62.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in z around 0 89.8%

      \[\leadsto x + \frac{y}{\color{blue}{-1 \cdot \frac{a - t}{t}}} \]
   6. Step-by-step derivation

      1. associate-*r/ 89.8%

         \[\leadsto x + \frac{y}{\color{blue}{\frac{-1 \cdot \left(a - t\right)}{t}}} \]

      2. neg-mul-1 89.8%

         \[\leadsto x + \frac{y}{\frac{\color{blue}{-\left(a - t\right)}}{t}} \]

   7. Simplified 89.8%

      \[\leadsto x + \frac{y}{\color{blue}{\frac{-\left(a - t\right)}{t}}} \]

   8. Taylor expanded in y around 0 56.5%

      \[\leadsto x + \color{blue}{\frac{t \cdot y}{t - a}} \]
   9. Step-by-step derivation

      1. associate-/l* 89.7%

         \[\leadsto x + \color{blue}{\frac{t}{\frac{t - a}{y}}} \]

   10. Simplified 89.7%

       \[\leadsto x + \color{blue}{\frac{t}{\frac{t - a}{y}}} \]
3. Recombined 3 regimes into one program.

4. Final simplification 89.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -6.5 \cdot 10^{+186}:\\ \;\;\;\;x + y\\ \mathbf{elif}\;t \leq 3.2 \cdot 10^{+123}:\\ \;\;\;\;x + z \cdot \frac{y}{a - t}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{t}{\frac{t - a}{y}}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 76.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.024 \lor \neg \left(t \leq 0.32\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.024) (not (<= t 0.32))) (+ x y) (+ x (* y (/ z a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.024) || !(t <= 0.32)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-0.024d0)) .or. (.not. (t <= 0.32d0))) then
        tmp = x + y
    else
        tmp = x + (y * (z / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.024) || !(t <= 0.32)) {
		tmp = x + y;
	} else {
		tmp = x + (y * (z / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.024) or not (t <= 0.32):
		tmp = x + y
	else:
		tmp = x + (y * (z / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.024) || !(t <= 0.32))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(y * Float64(z / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.024) || ~((t <= 0.32)))
		tmp = x + y;
	else
		tmp = x + (y * (z / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.024], N[Not[LessEqual[t, 0.32]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(y * N[(z / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.024 or 0.320000000000000007 < t

   1. Initial program 72.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 73.7%

         \[\leadsto \color{blue}{y + x} \]

   7. Simplified 73.7%

      \[\leadsto \color{blue}{y + x} \]

   if -0.024 < t < 0.320000000000000007

   1. Initial program 94.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 95.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 95.7%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. clear-num 95.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y}}} \]

      2. associate-/r/ 95.7%

         \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{z - t}} \cdot y} \]

      3. clear-num 95.8%

         \[\leadsto x + \color{blue}{\frac{z - t}{a - t}} \cdot y \]

   6. Applied egg-rr 95.8%

      \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot y} \]

   7. Taylor expanded in t around 0 79.4%

      \[\leadsto x + \color{blue}{\frac{z}{a}} \cdot y \]
3. Recombined 2 regimes into one program.

4. Final simplification 76.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.024 \lor \neg \left(t \leq 0.32\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + y \cdot \frac{z}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 76.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -0.055 \lor \neg \left(t \leq 0.011\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -0.055) (not (<= t 0.011))) (+ x y) (+ x (* z (/ y a)))))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.055) || !(t <= 0.011)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-0.055d0)) .or. (.not. (t <= 0.011d0))) then
        tmp = x + y
    else
        tmp = x + (z * (y / a))
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -0.055) || !(t <= 0.011)) {
		tmp = x + y;
	} else {
		tmp = x + (z * (y / a));
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -0.055) or not (t <= 0.011):
		tmp = x + y
	else:
		tmp = x + (z * (y / a))
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -0.055) || !(t <= 0.011))
		tmp = Float64(x + y);
	else
		tmp = Float64(x + Float64(z * Float64(y / a)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -0.055) || ~((t <= 0.011)))
		tmp = x + y;
	else
		tmp = x + (z * (y / a));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -0.055], N[Not[LessEqual[t, 0.011]], $MachinePrecision]], N[(x + y), $MachinePrecision], N[(x + N[(z * N[(y / a), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if t < -0.0550000000000000003 or 0.010999999999999999 < t

   1. Initial program 72.0%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 99.9%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.7%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 73.7%

         \[\leadsto \color{blue}{y + x} \]

   7. Simplified 73.7%

      \[\leadsto \color{blue}{y + x} \]

   if -0.0550000000000000003 < t < 0.010999999999999999

   1. Initial program 94.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 95.7%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 95.7%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around 0 77.5%

      \[\leadsto \color{blue}{x + \frac{y \cdot z}{a}} \]
   6. Step-by-step derivation

      1. +-commutative 77.5%

         \[\leadsto \color{blue}{\frac{y \cdot z}{a} + x} \]

      2. associate-/l* 79.4%

         \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}}} + x \]

   7. Simplified 79.4%

      \[\leadsto \color{blue}{\frac{y}{\frac{a}{z}} + x} \]
   8. Step-by-step derivation

      1. associate-/r/ 81.4%

         \[\leadsto \color{blue}{\frac{y}{a} \cdot z} + x \]

   9. Applied egg-rr 81.4%

      \[\leadsto \color{blue}{\frac{y}{a} \cdot z} + x \]
3. Recombined 2 regimes into one program.

4. Final simplification 78.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -0.055 \lor \neg \left(t \leq 0.011\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x + z \cdot \frac{y}{a}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 62.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-83} \lor \neg \left(t \leq 2.6 \cdot 10^{+110}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a)
 :precision binary64
 (if (or (<= t -5.5e-83) (not (<= t 2.6e+110))) (+ x y) x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.5e-83) || !(t <= 2.6e+110)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if ((t <= (-5.5d-83)) .or. (.not. (t <= 2.6d+110))) then
        tmp = x + y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if ((t <= -5.5e-83) || !(t <= 2.6e+110)) {
		tmp = x + y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if (t <= -5.5e-83) or not (t <= 2.6e+110):
		tmp = x + y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if ((t <= -5.5e-83) || !(t <= 2.6e+110))
		tmp = Float64(x + y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if ((t <= -5.5e-83) || ~((t <= 2.6e+110)))
		tmp = x + y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[Or[LessEqual[t, -5.5e-83], N[Not[LessEqual[t, 2.6e+110]], $MachinePrecision]], N[(x + y), $MachinePrecision], x]

Derivation

1. Split input into 2 regimes

2. if t < -5.49999999999999964e-83 or 2.6e110 < t

   1. Initial program 71.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 73.5%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 73.5%

         \[\leadsto \color{blue}{y + x} \]

   7. Simplified 73.5%

      \[\leadsto \color{blue}{y + x} \]

   if -5.49999999999999964e-83 < t < 2.6e110

   1. Initial program 95.8%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 95.6%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 95.6%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 52.1%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \leq -5.5 \cdot 10^{-83} \lor \neg \left(t \leq 2.6 \cdot 10^{+110}\right):\\ \;\;\;\;x + y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 97.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + y \cdot \frac{z - t}{a - t} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (* y (/ (- z t) (- a t)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (a - t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y * ((z - t) / (a - t)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y * ((z - t) / (a - t)));
}

Python

def code(x, y, z, t, a):
	return x + (y * ((z - t) / (a - t)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y * Float64(Float64(z - t) / Float64(a - t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y * ((z - t) / (a - t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y * N[(N[(z - t), $MachinePrecision] / N[(a - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 84.6%

   \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-/l* 97.6%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

3. Simplified 97.6%

   \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
4. Add Preprocessing
5. Step-by-step derivation

   1. clear-num 97.5%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{\frac{a - t}{z - t}}{y}}} \]

   2. associate-/r/ 97.6%

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a - t}{z - t}} \cdot y} \]

   3. clear-num 97.6%

      \[\leadsto x + \color{blue}{\frac{z - t}{a - t}} \cdot y \]

6. Applied egg-rr 97.6%

   \[\leadsto x + \color{blue}{\frac{z - t}{a - t} \cdot y} \]

7. Final simplification 97.6%

   \[\leadsto x + y \cdot \frac{z - t}{a - t} \]
8. Add Preprocessing

Alternative 13: 51.7% accurate, 1.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+153}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (if (<= y -1.55e+153) y x))

C

double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.55e+153) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    real(8) :: tmp
    if (y <= (-1.55d+153)) then
        tmp = y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	double tmp;
	if (y <= -1.55e+153) {
		tmp = y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y, z, t, a):
	tmp = 0
	if y <= -1.55e+153:
		tmp = y
	else:
		tmp = x
	return tmp

Julia

function code(x, y, z, t, a)
	tmp = 0.0
	if (y <= -1.55e+153)
		tmp = y;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y, z, t, a)
	tmp = 0.0;
	if (y <= -1.55e+153)
		tmp = y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_, z_, t_, a_] := If[LessEqual[y, -1.55e+153], y, x]

Derivation

1. Split input into 2 regimes

2. if y < -1.55e153

   1. Initial program 53.7%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 99.8%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in t around inf 31.3%

      \[\leadsto \color{blue}{x + y} \]
   6. Step-by-step derivation

      1. +-commutative 31.3%

         \[\leadsto \color{blue}{y + x} \]

   7. Simplified 31.3%

      \[\leadsto \color{blue}{y + x} \]

   8. Taylor expanded in y around inf 31.5%

      \[\leadsto \color{blue}{y} \]

   if -1.55e153 < y

   1. Initial program 89.3%

      \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
   2. Step-by-step derivation

      1. associate-/l* 97.2%

         \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

   3. Simplified 97.2%

      \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf 56.0%

      \[\leadsto \color{blue}{x} \]
3. Recombined 2 regimes into one program.

4. Final simplification 52.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+153}:\\ \;\;\;\;y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 14: 50.2% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ x \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 x)

C

double code(double x, double y, double z, double t, double a) {
	return x;
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x;
}

Python

def code(x, y, z, t, a):
	return x

Julia

function code(x, y, z, t, a)
	return x
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x;
end

Wolfram

code[x_, y_, z_, t_, a_] := x

Derivation

1. Initial program 84.6%

   \[x + \frac{y \cdot \left(z - t\right)}{a - t} \]
2. Step-by-step derivation

   1. associate-/l* 97.6%

      \[\leadsto x + \color{blue}{\frac{y}{\frac{a - t}{z - t}}} \]

3. Simplified 97.6%

   \[\leadsto \color{blue}{x + \frac{y}{\frac{a - t}{z - t}}} \]
4. Add Preprocessing

5. Taylor expanded in x around inf 49.7%

   \[\leadsto \color{blue}{x} \]

6. Final simplification 49.7%

   \[\leadsto x \]
7. Add Preprocessing

Developer target: 98.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ x + \frac{y}{\frac{a - t}{z - t}} \end{array} \]

FPCore

(FPCore (x y z t a) :precision binary64 (+ x (/ y (/ (- a t) (- z t)))))

C

double code(double x, double y, double z, double t, double a) {
	return x + (y / ((a - t) / (z - t)));
}

Fortran

real(8) function code(x, y, z, t, a)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8), intent (in) :: z
    real(8), intent (in) :: t
    real(8), intent (in) :: a
    code = x + (y / ((a - t) / (z - t)))
end function

Java

public static double code(double x, double y, double z, double t, double a) {
	return x + (y / ((a - t) / (z - t)));
}

Python

def code(x, y, z, t, a):
	return x + (y / ((a - t) / (z - t)))

Julia

function code(x, y, z, t, a)
	return Float64(x + Float64(y / Float64(Float64(a - t) / Float64(z - t))))
end

MATLAB

function tmp = code(x, y, z, t, a)
	tmp = x + (y / ((a - t) / (z - t)));
end

Wolfram

code[x_, y_, z_, t_, a_] := N[(x + N[(y / N[(N[(a - t), $MachinePrecision] / N[(z - t), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024096 
(FPCore (x y z t a)
  :name "Graphics.Rendering.Plot.Render.Plot.Axis:renderAxisTicks from plot-0.2.3.4, B"
  :precision binary64

  :herbie-target
  (+ x (/ y (/ (- a t) (- z t))))

  (+ x (/ (* y (- z t)) (- a t))))